Stochastic problems are defined by algebraic, differential or integral equations with random coefficients and/or input. However, it is the type, rather than the particular field of application, that is used to categorize these problems. An introductory chapter outlines the types of stochastic problems under consideration in this book and illustrates some of their applications. A user-friendly, systematic exposition unfolds as follows: the ...

This book accounts in 5 independent parts, recent main developments of Stochastic Analysis: Gross-Stroock Sobolev space over a Gaussian probability space; quasi-sure analysis; anticipate stochastic integrals as divergence operators; principle of transfer from ordinary differential equations to stochastic differential equations; Malliavin calculus and elliptic estimates; stochastic Analysis in infinite dimension. TOC:Contents: Part I. ...

Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, ...

In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises. The author, a specialist of classical stochastic calculus and martingale theory, tries to provide an introduction to this rapidly expanding field in a way which should be accessible to probabilists familiar with the Ito integral. It can also, on the other hand, ...

Interactive Particle Systems is a branch of Probability Theory with close connections to Mathematical Physics and Mathematical Biology. In 1985, the author wrote a book (T. Liggett, Interacting Particle System, ISBN 3-540-96069) that treated the subject as it was at that time. The present book takes three of the most important models in the area, and traces advances in our understanding of them since 1985. In so doing, many of the most useful ...

This volume contains selected papers presented at a UK-Japanese Workshop held at Churchill College, Cambridge, July 1995. The first group of papers looks at modelling, and solution techniques that have proved useful in the operational and strategic levels of manufacturing-greedy algorithms, Markov Decision processes and Petri Nets. Further papers concentrate on operational aspects of manufacturing in an uncertain environment. The last group ...

Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios and for analyzing the effects induced on the behavior of these portfolios by changes in the distribution of capital in the market.Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics and to determine the ...

The book provides an easily accessible computationally oriented introduction into the numerical solution of stochastic differential equations using computer experiments. It develops in the reader an ability to apply numerical methods solving stochastic differential equations in their own fields. Furthermore, it creates an intuitive understanding of the necessary theoretical background from stochastic and numeric analysis. A downloadable softward ...

This volume deals with Stochastic tools with special
reference to applications in the areas of Physics, Biology
and Operations Research. Quitea few of the papers deal with
the applications of the rich theory of point processes in
Physics and Operations Research. A few of the papers deal
with the problems of Inference and Stochastic theory. In
addition papers of some leading specialists are included.
These papers ...

In many areas of finance and stochastics, significant advances have been made since this field of research was opened by Black, Scholes and Merton in 1973. Advances in Finance and Stochastics contains a collection of original articles by a number of highly distinguished authors on research topics that are currently in the focus of interest of both academics and practitioners. The topics span risk management, portfolio theory and multi-asset ...